In algebraic number theory, the conductor of a finite abelian extension of local or global fields provides a quantitative measure of the ramification...

disorder Conductor (ring theory) Conductor of an abelian variety Conductor of a Dirichlet character Conductor (class field theory) Artin conductor, of a...

equivalence classes of binary quadratic forms of a given discriminant. 4.  The class number problem. conductor Conductor (class field theory) coprime Two...

In algebraic number theory, a quadratic field is an algebraic number field of degree two over Q {\displaystyle \mathbf {Q} } , the rational numbers. Every...

mathematics, the Artin conductor is a number or ideal associated to a character of a Galois group of a local or global field, introduced by Emil Artin (1930...

In number theory, the class number formula relates many important invariants of an algebraic number field to a special value of its Dedekind zeta function...

variety over a local field and proves it for a curve. The deepest result about the Bloch conductor is its equality with the Artin conductor, defined in terms...

1927; 1930), is a general theorem in number theory that forms a central part of global class field theory. The term "reciprocity law" refers to a long...

example the quadratic fields have as conductor the absolute value of their discriminant, a fact generalised in class field theory. The theorem was first...

electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases gradually...

Dirichlet character of conductor 1. The number of Hilbert characters is the order of the class group of the field. Class field theory identifies the Hilbert...

production of an electromotive force (emf) across an electrical conductor in a changing magnetic field. Michael Faraday is generally credited with the discovery...

algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local class field theory and diophantine...

definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations....

potential Moving magnet and conductor problem Wheeler–Feynman absorber theory Paradox of a charge in a gravitational field Kargon, Robert; Achinstein,...

specifically the area of algebraic number theory, a cubic field is an algebraic number field of degree three. If K is a field extension of the rational numbers...

ground itself can be used as one conductor of the circuit, saving the cost of installing a separate return conductor (see single-wire earth return and...

Bibcode:2010arXiv1011.6283M Schoof, René (2003), "Class numbers of real cyclotomic fields of prime conductor", Mathematics of Computation, 72 (242): 913–937...

high ionic conductivity in the relatively safer and more stable class of oxide conductors. The authors showed that oxides (which typically do not crystallize...

Jean-Pierre (1967), "Local class field theory", in Cassels, J. W. S.; Fröhlich, Albrecht (eds.), Algebraic Number Theory, Proceedings of an instructional...

According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are...

the exterior field increases. The experiment demonstrated for the first time that superconductors were more than just perfect conductors and provided...

Galois extension L / K {\displaystyle L/K} of local or global fields from the Artin conductors of the irreducible characters I r r ( G ) {\displaystyle \mathrm...

Basic Number Theory is an influential book by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on valuation-theoretic...

quanta of the electromagnetic field, responsible for all electromagnetic interactions. Quantum electrodynamics is the theory of how EMR interacts with matter...

map, is a crucial ingredient of class field theory, which studies the finite abelian extensions of a given number field K. In the geometric analogue, for...

constant along the conductor, so it acts as a simple connector which transfers alternating current with negligible phase shift. In circuit theory the connecting...

becomes a conductor, causing a large increase in current, an electric arc through the substance. Electrical breakdown occurs when the electric field in the...

field combined with an electric field can distinguish between these, see Hall effect below. The first term in the Lorentz equation is from the theory...

fields, then the notions of "integral over" and of an "integral extension" are precisely "algebraic over" and "algebraic extensions" in field theory (since...